Optimal Waveform for the Entrainment of a Weakly Forced Oscillator

Takahiro Harada, Hisa-Aki Tanaka, Michael J. Hankins, and István Z. Kiss
Physical Review Letters, vol. 105, no. 8, 088301, Aug. 2010.


A theory for obtaining a waveform for the effective entrainment of a weakly forced oscillator is presented. Phase model analysis is combined with calculus of variation to derive a waveform with which entrainment of an oscillator is achieved with a minimum power forcing signal. Optimal waveforms are calculated from the phase response curve and a solution to a balancing condition. The theory is tested in chemical entrainment experiments in which oscillations close to and farther away from a Hopf bifurcation exhibited sinusoidal and higher harmonic nontrivial optimal waveforms, respectively.

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